{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

homework_1

# homework_1 - ELECTRODYNAMICS PROBLEM SET 1 due February 2nd...

This preview shows pages 1–2. Sign up to view the full content.

ELECTRODYNAMICS PROBLEM SET 1 due February 2nd, before class Problem 1.: tensor (anti)-symmetry Show that if A μν = A νμ is a symmetric tensor in one frame, it’ll be symmetric in any other frame. Is anti -symmetry ( A μν = - A νμ ) also frame independent? Show that if S μν is symmetric ( S μν = S νμ ) and A μν is antisymmetric ( A μν = - A νμ ) then A μν S μν = 0. Show that ∇ × ∇ f = 0 , . ∇ × ~a = 0 , (1) for sufficiently well-behaved f and ~a . Problem 2.: Most of vector/tensor analysis The index notation discussed in class is very useful, eve if all you want to do is to deal with vectors (not tensors) in 3D. But you need a little practice to use it efficiently. Instead of memorizing all those identities you find on the back of textbooks, you need only the fundamental relation ijk ilm = δ jl δ km - δ jm δ kl . (2) Show the relation above (hint: what else could the right-hand side be?). It is then easy to show ijk ijm = 2 δ km (3) Now you are ready to show c) Show that ~ A. ( ~ B × ~ C ) = ~ B. ( ~ C × ~ A ) = ~ C. ( ~ A × ~ B ) (4) ( ~ A.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern